And here's a yet another "slightly cleaner" version:

   interp4=: 2 : '({. (1+m) difftb n)  +/ .* ((i.1+m)&(!/))'
   3 interp4 data
0 1 6 6 +/ .* 0 1 2 3&(!/)

FYI,

-- 
Raul
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